Cardiac and, more generally, dynamic imaging is one of the top challenges facing modern computed tomography. When the object being scanned changes during data acquisition the classic tomographic reconstruction theory does not apply. In cardiac computed tomography there are two major groups of approaches for dealing with this issue. One is based on gating, i.e., selecting the computed tomography data which correspond to a fixed cardiac phase, and then using mostly that data for image reconstruction. The second approach, known as motion compensation, is based on incorporating a motion model into a reconstruction algorithm. Motion compensation algorithms are preferable, because they use all data and have the potential to provide good image quality with reduced x-ray dose. The main difficulty of using such algorithms is that the motion model needs to be known. There are motion estimation algorithms available, but significant research still needs to be done to improve efficiency, accuracy, and stability with respect to noise, flexibility, and the like.
The methods and systems of the present invention solve the problems associated with the prior art using a novel approach to motion estimation, which is based on local tomography (LT). The ultimate goal is a robust algorithm which can reconstruct objects that change during the scan. Since there is no formula that recovers the object f and motion function ψ from the tomographic data, the most realistic approach to finding f and ψ is via iterations. On the other hand, recovering both of them at the same time would result in an iterative problem of a prohibitively large size.
The best approach is to decouple the two tasks, motion estimation and motion compensation, as much as possible. Not all methods achieve this goal. For example, when finding ψ using registration, one uses the images of f at different times. In other words, finding ψ depends on the knowledge of f. This has undesirable consequences. When motion is not known, f is reconstructed with significant artifacts, making subsequent registration unreliable and inaccurate. In contrast, LT is an ideal candidate for decoupling. LT does not reconstruct pointwise values of f, but rather a gradient-like image of f with edges enhanced. Thus the only informative feature of LT is the location of edges.